Wavelength From Frequency

Question

A television transmitter broadcasts at a frequency of 6.0 × 10⁸ Hz, and a technician must determine the wavelength of the emitted signal in free space.

RankGuru · Accepted Answer

Grounded in NCERT Class 12, Chapter 8 (Electromagnetic Waves), the wavelength of an electromagnetic wave in free space is obtained from λ = c/f, since all such waves travel at the speed of light c = 3 × 10⁸ m/s. The broadcast signal is a radio-frequency electromagnetic wave that needs no medium to propagate. Substituting the given frequency: λ = (3 × 10⁸)/(6.0 × 10⁸) = 0.5 m, a typical metre-scale wavelength for such transmissions. The value 2.0 m is incorrect because it inverts the ratio, dividing frequency by speed instead of speed by frequency in the wrong sense. The value 18 m arises from multiplying speed and frequency and mishandling powers of ten. The value 0.05 m results from a decimal-place slip, misplacing one power of ten in the division. A magnitude check confirms that a signal near 600 MHz should have a sub-metre wavelength, consistent with the calculated 0.5 m, so that answer is validated.

Wavelength From Frequency

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